Coherent terahertz (THz) detection methods, such as terahertz time-domain spectroscopy (THz-TDS), allow the spectroscopy of materials without assuming the Kramers-Kronig relation [1]. Since the spectral resolution in terahertz time-domain spectroscopy (THz-TDS) depends on the length of the scan (Δv=1/T), long scanning times are required to achieve high spectral resolution. Various methods, such as photoconductive antennas [2], electro-optic (EO) sampling, air-biased-coherent-detection (ABCD) [3] and spectral domain interferometry (SDI) [4-5] have been demonstrated for measuring the temporal THz electric field profile. Among these methods, the electro-optic (EO) sampling method has become most common due to its simplicity [6].
In electro-optic (EO) sampling, a linearly polarized femtosecond laser pulse co-propagates with a picosecond THz pulse in an electro-optic (EO) crystal. The THz electric field induces birefringence in the crystal, which changes the polarization of the linearly co-propagating laser pulse. The change in the phase between the two polarization components of the probe beam, which is proportional to the THz electric field, can be measured by using a quarter-wave plate and a Wollaston polarizer placed after the detection crystal. In this case, the phase change appears as a modulation in the intensity of the probe beam. The complete THz waveform can be reconstructed by scanning the probe pulse over the entire THz pulse.
Several improvements in electro-optic (EO) sampling have been proposed, such as the chirped-pulse or spectral-encoding method [7], the cross-correlation method [8], the two dimensional THz pulse characterization method with dual echelons [9], and the tilted wavefront detection method using prisms [10].
To obtain high spectral resolution for spectroscopic purposes, a long scanning time is required, which is typically achieved by using thicker detection crystals. If a thin crystal is used, internal reflections from the two surfaces of the crystal interfere with the main detected THz signal, which induces unwanted beating in the measured spectrum.
All the aforementioned THz detection methods based on electro-optic (EO) sampling have used a quarter-wave plate and a Wollaston prism to measure the THz electric field. However, with recent advances in high power THz generation methods, the use of thicker crystals poses a so called “over-rotation” issue. If the THz electric field is high enough to introduce a phase difference of more than 90°, a reversal in the intensity modulation of the detection beam occurs, leading to ambiguities in the measured THz field [11], a situation referred to as “over-rotation”. Birefringence introduced in the electro-optic (EO) crystal is proportional to both the THz electric field and the thickness of the crystal. In principle thinner crystals could be used to avoid over-rotation, but thinner crystals cause internal reflection effects, as discussed hereinabove. Moreover, the use of thin crystals reduces the signal-to-noise ratio (SNR) of the measured THz signal, due to the decrease in interaction length.
The air-biased-coherent-detection (ABCD) method [3] does not have the problem of over-rotation, but the need for a high voltage supply makes it more complicated to use when compared with the electro-optic (EO) sampling methods, and the use of plasma for detection is intrinsically unstable.
Therefore, a simple method is yet desirable to satisfy the requirement for measuring intense THz electric fields.
To allow long scans in time, with the goal to improve spectral resolution and to avoid over-rotation for intense THz pulses, a method based on spectral domain interferometry (SDI) has been proposed. In this method, change in the phase difference introduced in the probe beam due to the THz electric field is measured using spectral domain interferometry (SDI).
The spectral domain interferometry (SDI) method has already been used to measure phase changes as small as few micro-radians for various other applications [12]. The spectral domain interferometry (SDI) method not only has the ability to measure intense THz electric fields for spectroscopic purposes with good spectral resolution, but also simplifies the setup by eliminating the need for lock-in amplifiers. It also allows the use of thick detection crystals by solving the problem of over-rotation for high-power THz sources.
Details on the use of spectral domain interferometry (SDI) for measuring small phase changes have been described in previous works [13-15]. Here only a brief overview of this method is given for the sake of completeness. In conventional spectral domain interferometry (SDI), a broadband light source of bandwidth Δλ centered around λ0 is used to illuminate a reference surface and the sample surface in a Michelson interferometer scheme. The reflected signals from the reference and the sample surfaces, with intensities IR and IS respectively, are spectrally dispersed over a charged-coupled device (CCD) camera using a grating to yield an interference signal that can be represented by:I(k)=IR(k)+IS(k)+2√{square root over (IR(k)IS(k))} cos [ϕ0+2kL]  (1)where k=2π/λ is the wave vector, ϕ0 is a phase constant and L is the optical path difference (OPD) between the reference signal and the sample signal.
The instantaneous phase difference between the reference surface and the sample surface is determined using the following relation:
                    ϕ        =                  arctan          ⁢                                          ⁢                      (                                          Im                ⁢                                                                                          ⁢                                                                                        (                                                      I                    ~                                    ⁡                                      (                    L                    )                                                  )                                            Re                ⁢                                                                  ⁢                                  (                                                            I                      ~                                        ⁡                                          (                      L                      )                                                        )                                                      )                                              (        2        )            where Ĩ(L) is the Fourier transform of relation (1) above.
Thus, any change in the optical path difference over time can be tracked [15] by monitoring the phase change given by relation (2).
A spectral domain interferometry (SDI) detection set up as proposed in PCT patent application WO 2014/019091 is shown in FIG. 1. A beam splitter (BS1) divides a laser beam into a probe beam and a pump beam. The pump beam is used to generate the THz signal. A beam splitter (BS2) divides the probe beam further into two equal parts. The reflected part of the probe beam is sent to a 0.3 mm-thick glass plate. The two surfaces of the glass plate each reflect about 4% of the incident beam. Half of the probe beam that is reflected from the glass plate is transmitted through the beam splitter (BS2). The reflected signal from the glass plate consists of two pulses, a front pulse that is reflected from the front surface, and a back pulse reflected from the back surface of the glass plate. The front pulse and the back pulse are separated by 3 ps, due to the refractive index of 1.5 associated with the glass plate. Using a cylindrical lens (CL1), these two pulses propagate through a hole in an off-axis mirror, and their line-like spatial profile is focused onto a 0.5 mm thick ZnTe detection crystal, overlapping the THz beam. A cylindrical lens (CL2) is used to collimate the probe beam, which is then sent to a spectrometer. A typical custom made spectrometer consists of a grating, with 600 grooves/mm, a cylindrical lens, with a focal length f=100 mm, and a 2D charged-coupled device (CCD) camera (PixeLINK, PL-B953) with 760×1024 pixels.
Using the spectrometer, interference fringes in the spectrum are observed due to the interference between the front and back pulses. In spectral domain interferometry (SDI), the different spectral components of the beam are separated after the diffraction grating, and thus the various spectral components of the probe pulse are not mode locked any more. This is why the interference pattern can be measured over the depth range of the spectral domain interferometry (SDI) method, as determined by the spectrometer used. For a Gaussian profiled spectrum, the depth range can be written as follows:
                              d          max                =                                            2              ⁢                                                          ⁢              ln              ⁢                                                          ⁢              2                        π                    ⁢                      N            2                    ⁢                                    λ              0              2                                      Δ              ⁢                                                          ⁢              λ                                                          (        3        )            
To measure the complete THz pulse, an optical delay line is used to vary the delay between the THz pulse and the optical pulse. The THz pulse is temporally matched with the optical back probe pulse. The delay between the front pulse and the back pulse is large enough, i.e. 3 ps, so that the front pulse can pass through the ZnTe crystal without seeing the THz electric field. The presence of the THz electric field changes the refractive index of the ZnTe crystal via the Pockels effect. The back pulse experiences this change in the refractive index, while the front pulse does not, thus introducing a phase difference between the two optical probe pulses. This phase change between the two optical probe pulses is proportional to the THz electric field. Therefore, the shape of the THz electric field can be reconstructed by changing the delay between the THz and the probe pulse. In the spectral domain interferometry (SDI) method, the change in the phase introduced by the change in the refractive index of the ZnTe crystal is measured, from which the THz electric field can be measured up to the depth range of the spectral domain interferometry (SDI) method.
To reconstruct the THz signal, data from the camera are numerically treated, which involves several intermediate steps. These steps are as follows. The data from the camera, acquired in the wavelength space, are rescaled to the wave vector (k)-space. Then, they are Fourier transformed to obtain the frequency corresponding to the optical path difference between the two signals reflected from the glass plate. The phase difference between these two pulses reflected from the glass plate is measured using Relation (1) above. This phase is tracked over time while changing the delay between the THz signal and the probing signal. The phase waveform gives the waveform of the THz electric field.
The spectral domain interferometry (SDI) method described hereinabove has overcome several problems that exist in other THz detection methods, most notably over-rotation and complex setups. However, the scan length is limited by the thickness of the glass plate, which in the system discussed in relation to FIG. 1 was 3 ps, with a glass plate with a thickness of 0.3 mm, whereas there are many cases when longer scans would be necessary to resolve the fine spectrum. As for signal-to-noise ratio (SNR), results of THz electric field measured using spectral domain interferometry (SDI) and electro-optic (EO) sampling show that the signal-to-noise ratio (SNR) is lower with spectral domain interferometry (SDI) than with electro-optic (EO) sampling. This is partially because of vibrations in the experimental environment, which changes the angle between the probe beam and the glass plate, thus introducing noise to the phase. The spectral domain interferometry (SDI) signal is also affected by the strong background near zero optical path difference, which significantly reduces the signal-to-noise ratio (SNR).
It thus appears that conventional THz detection methods, such as electro-optic (EO) sampling and the air-biased-coherent-detection (ABCD) method for example, suffer from over-rotation effects and/or have a complex configuration, while the more recent spectral domain interferometry (SDI) method discussed hereinabove needs be improved as far as measuring long scans and signal-to-noise ratio (SNR) are concerned.
In the spectral domain interferometry (SDI) method, the scan length can be increased by using a thicker glass plate, whose thickness is within the depth range of the spectral domain interferometry (SDI) system. A Mach-Zehnder-type interferometer configuration can also be used to increase the overlap between the reference and the probe pulse. The signal-to-noise ratio (SNR) can be improved by using a low readout noise camera. The self-referencing method can also be used in the spectral domain interferometry (SDI) detection, where the optical probe beam is focused at the detection crystal in a line-like pattern. This line can be imaged back on to the 2D charged-coupled device (CCD) camera along the vertical direction i.e. perpendicular to the diffraction plane of the grating in the spectrometer. This way, the phase change or the optical path difference measured along the vertical direction of the charged-coupled device (CCD) camera gives the spatial profile of the THz signal.
Thus, as the art stands, in relation to scan length, using a thicker glass plate would increase the scan length, but this would also reduce the signal-to-noise ratio (SNR), due to the larger optical path difference between the two interfering signals [16]. The Mach-Zehnder-type interferometer configurations are more sensitive to vibrations, also resulting in larger noise in the measurement.
In relation to signal-to-noise ratio (SNR), even when using both a low readout noise camera and the self-referencing method in spectral domain interferometry (SDI) detection it is found that the signal-to-noise ratio (SNR) of spectral domain interferometry (SDI) measurements are much lower compared with those of electro-optic (EO) sampling.
There is still a need in the art for a method and system for characterization of terahertz radiation.